Transcript unit 2 Measurement Notes
Slide 1
MEASUREMENT
Cartoon courtesy of Lab-initio.com
Slide 2
2 types of measurement
Qualitative-a non-numerical description of matter.
(ex: red stone, heavy brick, hot steel)
Quantitative- a numerical measure. It must include a
number, followed by a unit.
(ex: 2.14 grams, 49.6 ml, 0.2500 kg)
Slide 3
Uncertainty in Measurement
A digit that must be estimated
is called uncertain. A
measurement always has some
degree of uncertainty.
Slide 4
Why Is there Uncertainty?
Measurements are performed with
instruments
No instrument can read to an infinite
number of decimal places
Which of these balances has the greatest
uncertainty in measurement?
Slide 5
Taking Measurements
When taking measurements:
Read to the smallest increment(mark) on the
instrument
Estimate one digit past the smallest increment(mark)
Slide 6
Reading the Graduated
Cylinder
Liquids in glass and some
plastic containers curve at
the edges
Changing the diameter of the
cylinder will change the
shape of the curve
This curve is called the
MENISCUS
Slide 7
Reading the Graduated
Cylinder
Your eye should be level with
the top of the liquid
You should
read to the
bottom of
the
MENISCUS
Slide 8
Use the smallest increments to find all
certain digits, then estimate 1 more digit.
There are two
unlabeled
graduations
below the
meniscus, and
each graduation
represents 1 mL,
so the certain
digits of the
reading are…
mL.
Slide 9
Estimate the uncertain digit and
take a reading
The meniscus is
about eight
tenths of the
way to the next
graduation, so
the final 0.8
digit
mLin
the reading is
.
The volume in the graduated
cylinder is
mL.
Slide 10
10 mL Graduated Cylinder
What is the volume of liquid in the
graduate?
___mL
Slide 11
25mL graduated cylinder
What is the volume of liquid in the
graduate?
___mL
Slide 12
100mL graduated cylinder
What is the volume of liquid in the
graduate?
____mL
Slide 13
Practice Reading the
Graduated Cylinder
What is
this
reading?
___ ml
Slide 14
Practice Reading the
Graduated Cylinder
What is
this
reading?
____ ml
Slide 15
What is the volume of water in each cylinder?
Pay attention to the scales for each cylinder.
Images created at http://www.standards.dfes.gov.uk/primaryframework/downloads/SWF/measuring_cylinder.swf
Measuring Liquid Volume
Slide 16
Reading a graduated cylinder
All of the equipment below measures
volume in mL but the scales for each
are different.
___mL
____mL
___mL
Slide 17
Reading a Buret
On the graduated cylinder, zero was
at the bottom of the scale, with
values increasing going up the
cylinder. However, a buret has
zero at the top with values
increasing going down the scale.
Determine the scale.
Read at the bottom of the meniscus
with your eye level with the liquid.
____mL
Slide 18
What is the volume in the buret?
Slide 19
What is the volume in the buret?
Slide 20
Slide 21
Slide 22
Slide 23
Online Practice
Reading a graduated cylinder
http://w1imr.cnm.edu/apps/chemlab/reading_a_meniscus.s
wf
Reading a buret
http://w1imr.cnm.edu/apps/chemlab/burette.swf
Reading a ruler
http://w1imr.cnm.edu/apps/chemlab/reading_a_ruler.swf
Slide 24
Lets play darts!
Slide 25
Precision and Accuracy
Accuracy how close a result is to its true value.
Precision refers to the repeatability of results.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Slide 26
Types of Error
Error- the difference between a measurement and
the accepted value.
Random Error - measurement has an equal
probability of being high or low.
Systematic Error – a repeated error,
often resulting from poor technique or
incorrect calibration.
Slide 27
Scientific
Notation
Slide 28
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Slide 29
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Slide 30
Scientific Notation:
A method of representing very large or
very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is the exponent
Slide 31
.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
Slide 32
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
Slide 33
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
Slide 34
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
Slide 35
Convert each standard number to
scientific notation:
2000 g
0.972 m
880000 m
6.55 s
0.00821 kg
71.9 ms
96.3 g
8999 cm
0.000965 m
450 g
Slide 36
Convert each to floating decimal form:
7.00 x 102 m
17 x 100 cm
2.22 x 10-4 cm
3.00 x 108 m/s
9.45 x 10-8 m
6.02 x 1023 atoms
4.00 x 103 g
8.75 x 10-1 m
5.99 x 10-5 kg
6.78 x 10-6 m
Slide 37
Significant Figures-all the
digits that are known to be
true.
Slide 38
Rules for Counting Significant
Figures - Details
Nonzero Digits(1-9) always count as
significant figures.
3456 has
4 significant figures
Slide 39
Rules for Counting Significant
Figures - Details
Zeros
- Leading zeros never count as
significant figures.
0.0486 has
3 significant figures
Slide 40
Rules for Counting Significant
Figures - Details
Zeros
Captive zeros(sandwiched zeros)
always count as significant figures.
-
16.07 has
4 significant figures
Slide 41
Rules for Counting Significant
Figures - Details
Zeros
Trailing zeros are significant only
if the number contains a decimal
point.
9.300 has
4 significant figures
Slide 42
Rules for Counting Significant
Figures - Details
Exact numbers have an infinite
number of significant figures. They
tend to be numbers of indivisible
objects.
7 computers
or
1 inch = 2.54 cm, exactly
Slide 43
Slide 44
Sig Fig Practice #1
How many significant figures in each of the following &
which is the estimated digit?
1.0070 m
5 sig figs(0)
17.10 kg
4 sig figs(0)
100,890 L
5 sig figs(9)
3.29 x 103 s
3 sig figs(9)
0.0054 cm
2 sig figs(4)
3,200,000
2 sig figs(2)
Slide 45
Rules for Significant Figures in
Mathematical Operations
Multiplication and Division: # sig figs in the
answer equals the least number of sig figs
used in the calculation.
6.38 cm x 2.0 cm =
12.76 13 cm2 (2 sig figs)
Slide 46
Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
0.358885017 g/mL
0.359 g/mL
Slide 47
Rules for Significant Figures in
Mathematical Operations
Addition and Subtraction: The number
of decimal places in the answer equals
the number of decimal places in the least
accurate measurement.
6.8 g + 11.934 g =
18.734 18.7 g (3 sig figs)
Slide 48
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
MEASUREMENT
Cartoon courtesy of Lab-initio.com
Slide 2
2 types of measurement
Qualitative-a non-numerical description of matter.
(ex: red stone, heavy brick, hot steel)
Quantitative- a numerical measure. It must include a
number, followed by a unit.
(ex: 2.14 grams, 49.6 ml, 0.2500 kg)
Slide 3
Uncertainty in Measurement
A digit that must be estimated
is called uncertain. A
measurement always has some
degree of uncertainty.
Slide 4
Why Is there Uncertainty?
Measurements are performed with
instruments
No instrument can read to an infinite
number of decimal places
Which of these balances has the greatest
uncertainty in measurement?
Slide 5
Taking Measurements
When taking measurements:
Read to the smallest increment(mark) on the
instrument
Estimate one digit past the smallest increment(mark)
Slide 6
Reading the Graduated
Cylinder
Liquids in glass and some
plastic containers curve at
the edges
Changing the diameter of the
cylinder will change the
shape of the curve
This curve is called the
MENISCUS
Slide 7
Reading the Graduated
Cylinder
Your eye should be level with
the top of the liquid
You should
read to the
bottom of
the
MENISCUS
Slide 8
Use the smallest increments to find all
certain digits, then estimate 1 more digit.
There are two
unlabeled
graduations
below the
meniscus, and
each graduation
represents 1 mL,
so the certain
digits of the
reading are…
mL.
Slide 9
Estimate the uncertain digit and
take a reading
The meniscus is
about eight
tenths of the
way to the next
graduation, so
the final 0.8
digit
mLin
the reading is
.
The volume in the graduated
cylinder is
mL.
Slide 10
10 mL Graduated Cylinder
What is the volume of liquid in the
graduate?
___mL
Slide 11
25mL graduated cylinder
What is the volume of liquid in the
graduate?
___mL
Slide 12
100mL graduated cylinder
What is the volume of liquid in the
graduate?
____mL
Slide 13
Practice Reading the
Graduated Cylinder
What is
this
reading?
___ ml
Slide 14
Practice Reading the
Graduated Cylinder
What is
this
reading?
____ ml
Slide 15
What is the volume of water in each cylinder?
Pay attention to the scales for each cylinder.
Images created at http://www.standards.dfes.gov.uk/primaryframework/downloads/SWF/measuring_cylinder.swf
Measuring Liquid Volume
Slide 16
Reading a graduated cylinder
All of the equipment below measures
volume in mL but the scales for each
are different.
___mL
____mL
___mL
Slide 17
Reading a Buret
On the graduated cylinder, zero was
at the bottom of the scale, with
values increasing going up the
cylinder. However, a buret has
zero at the top with values
increasing going down the scale.
Determine the scale.
Read at the bottom of the meniscus
with your eye level with the liquid.
____mL
Slide 18
What is the volume in the buret?
Slide 19
What is the volume in the buret?
Slide 20
Slide 21
Slide 22
Slide 23
Online Practice
Reading a graduated cylinder
http://w1imr.cnm.edu/apps/chemlab/reading_a_meniscus.s
wf
Reading a buret
http://w1imr.cnm.edu/apps/chemlab/burette.swf
Reading a ruler
http://w1imr.cnm.edu/apps/chemlab/reading_a_ruler.swf
Slide 24
Lets play darts!
Slide 25
Precision and Accuracy
Accuracy how close a result is to its true value.
Precision refers to the repeatability of results.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Slide 26
Types of Error
Error- the difference between a measurement and
the accepted value.
Random Error - measurement has an equal
probability of being high or low.
Systematic Error – a repeated error,
often resulting from poor technique or
incorrect calibration.
Slide 27
Scientific
Notation
Slide 28
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Slide 29
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Slide 30
Scientific Notation:
A method of representing very large or
very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is the exponent
Slide 31
.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
Slide 32
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
Slide 33
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
Slide 34
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
Slide 35
Convert each standard number to
scientific notation:
2000 g
0.972 m
880000 m
6.55 s
0.00821 kg
71.9 ms
96.3 g
8999 cm
0.000965 m
450 g
Slide 36
Convert each to floating decimal form:
7.00 x 102 m
17 x 100 cm
2.22 x 10-4 cm
3.00 x 108 m/s
9.45 x 10-8 m
6.02 x 1023 atoms
4.00 x 103 g
8.75 x 10-1 m
5.99 x 10-5 kg
6.78 x 10-6 m
Slide 37
Significant Figures-all the
digits that are known to be
true.
Slide 38
Rules for Counting Significant
Figures - Details
Nonzero Digits(1-9) always count as
significant figures.
3456 has
4 significant figures
Slide 39
Rules for Counting Significant
Figures - Details
Zeros
- Leading zeros never count as
significant figures.
0.0486 has
3 significant figures
Slide 40
Rules for Counting Significant
Figures - Details
Zeros
Captive zeros(sandwiched zeros)
always count as significant figures.
-
16.07 has
4 significant figures
Slide 41
Rules for Counting Significant
Figures - Details
Zeros
Trailing zeros are significant only
if the number contains a decimal
point.
9.300 has
4 significant figures
Slide 42
Rules for Counting Significant
Figures - Details
Exact numbers have an infinite
number of significant figures. They
tend to be numbers of indivisible
objects.
7 computers
or
1 inch = 2.54 cm, exactly
Slide 43
Slide 44
Sig Fig Practice #1
How many significant figures in each of the following &
which is the estimated digit?
1.0070 m
5 sig figs(0)
17.10 kg
4 sig figs(0)
100,890 L
5 sig figs(9)
3.29 x 103 s
3 sig figs(9)
0.0054 cm
2 sig figs(4)
3,200,000
2 sig figs(2)
Slide 45
Rules for Significant Figures in
Mathematical Operations
Multiplication and Division: # sig figs in the
answer equals the least number of sig figs
used in the calculation.
6.38 cm x 2.0 cm =
12.76 13 cm2 (2 sig figs)
Slide 46
Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
0.358885017 g/mL
0.359 g/mL
Slide 47
Rules for Significant Figures in
Mathematical Operations
Addition and Subtraction: The number
of decimal places in the answer equals
the number of decimal places in the least
accurate measurement.
6.8 g + 11.934 g =
18.734 18.7 g (3 sig figs)
Slide 48
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL